The stability and Hopf bifurcation for a kind of predator system with time delay is discussed. Appying Hurwitz discriminant method and eigenvalue theory, the sufficient condition of equilibrium being local asymptotic stability and the condition of Hopf bifurcation existence are obtained. By using Matlab software package, the fitting graph of solution curve is given. The feasibility of theorem conditions is also shown by an example.%讨论了一类时滞捕食系统的稳定性与Hopf分支问题.应用Hurwitz判别法及特征值理论得到平衡点局部渐近稳定的充分条件和Hopf分支存在的条件；利用Matlab给出了解曲线的拟合图,并举例验证了定理条件和结论的一致性.
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